Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing Adversary

Farhad Farokhi

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arXiv · 1904.07377

Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing Adversary

Farhad Farokhi

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Abstract

In this paper, we consider privacy against hypothesis testing adversaries within a non-stochastic framework. We develop a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic information theory. We define tests as binary-valued mappings on uncertain variables and prove a fundamental bound on the best performance of tests in non-stochastic hypothesis testing. We use this bound to develop a measure of privacy. We then construct reporting policies with prescribed privacy and utility guarantees. The utility of a reporting policy is measured by the distance between the reported and original values. We illustrate the effects of using such privacy-preserving reporting polices on a publicly-available practical dataset of preferences and demographics of young individuals, aged between 15-30, with Slovakian nationality.

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Farhad Farokhi. 2019-04-16. Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing Adversary. https://arxiv.org/abs/1904.07377

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